Iodide ion, as present in KI, does not decay. Period. It’s that ion that your body requires. The tablets would serve their purpose for long after they are purchased.
As a chemist, I will go ahead and inform you confidently that Potassium Iodide in a dry place will outlast you by a significant margin. It's very chemically stable.
Probably to account for people who won't store it properly, degradation of the packaging material, etc.
For example, if you store your blister pack of KI on a sunny shelf in your bathroom, UV rays eventually weaken the plastic packaging, cracks develop in the plastic letting in water vapor from your shower, and a stray mold space makes its way in as well and eventually you end up with mold growing on your pills. The KI itself may still be perfectly fine and able to do its job, but that mold might make you sick.
Idiodin itself can't get "bad" in any way. The carrier material might go bad, but that's also just starches and a few mineral compounds. At worst, you get powder instead of a pill.
The expiration dates on medication are intentionally extremely conservative.